Energy Efficient GPS Acquisition with Sparse-GPS · Energy Efficient GPS Acquisition with Sparse-GPS Prasant Misra , Wen Huy, Yuzhe Jinz, Jie Liuz, Amanda Souza de Paulax, Niklas

Energy Efficient GPS Acquisition with Sparse-GPS

Prasant Misra∗, Wen Hu†, Yuzhe Jin‡, Jie Liu‡, Amanda Souza de Paula§, Niklas Wirstrom¶, Thiemo Voigt¶‖∗Robert Bosch Center for Cyber Physical Systems, Indian Institute of Science, Bangalore, India

†CSIRO Computational Informatics, Brisbane, Australia‡Microsoft Research, Redmond, USA

§University of Sao Paulo, Sao Paulo, Brazil¶SICS Swedish ICT, Stockholm, Sweden‖Uppsala Universitet, Uppsala, Sweden

Email: [email protected]∗, [email protected]†, {yuzjin, jie}@microsoft.com‡,[email protected]§, {niwi,thiemo}@sics.se¶

Abstract—Following rising demands in positioning with GPS,low-cost receivers are becoming widely available; but their energydemands are still too high. For energy efficient GPS sensing indelay-tolerant applications, the possibility of offloading a fewmilliseconds of raw signal samples and leveraging the greaterprocessing power of the cloud for obtaining a position fix isbeing actively investigated. In an attempt to reduce the energycost of this data offloading operation, we propose Sparse-GPS1:a new computing framework for GPS acquisition via sparseapproximation. Within the framework, GPS signals can be effi-ciently compressed by random ensembles. The sparse acquisitioninformation, pertaining to the visible satellites that are embeddedwithin these limited measurements, can subsequently be recoveredby our proposed representation dictionary. By extensive empiricalevaluations, we demonstrate the acquisition quality and energygains of Sparse-GPS. We show that it is twice as energy efficientthan offloading uncompressed data, and has 5-10 times lowerenergy costs than standalone GPS; with a median positioningaccuracy of 40m.

Index Terms—GPS, synchronization, location sensing, energyefficiency, sparse approximation, compressed sensing

I. INTRODUCTION

Location is an important service in mobile sensing. Theglobal positioning system (GPS) is the most pervasive tech-nology that provides this fundamental service. The ubiquity ofGPS has, henceforth, grown beyond billions of smart phones toembedded devices for enabling many novel outdoor applica-tions across several domains. GPS receivers have, therefore,become more versatile in terms of cost, size and weight;but are still demanding in energy usage. It is an artifact ofthe computationally intensive GPS receiving operation, whichaccounts for more than 80% of the total energy expenditure ofthe sensing platform on which it is coupled [1]–[3].

The high energy profile is a combined effect of two primaryfactors. First, the GPS Ephemeris data, which contains the timeand satellite trajectory information, are sent by the satellites ata very low data rate of 50 bps. As a result, a standalone GPSreceiver needs to be turned on for up to 30 seconds in order toreceive a complete data packet from the satellite. Second, thetask of identifying and tracking the visible satellites, decodingtheir navigational information and performing the least-squarecalculation involves a significant amount of processing. It gets

1Prasant Misra∗ was a postdoctoral fellow, and Wen Hu† was a visitingresearcher at SICS Swedish ICT in Stockholm during the course of this work.

more intensive due to the weak GPS signal strengths (about20 dB below the noise level); and Doppler frequency shifts(≈ 4.2 kHz) caused by the satellite motion (and receiver move-ment on the ground) [4]. As a consequence, the first factormakes it difficult to duty-cycle the GPS receiver for savingenergy; while the second necessity introduces the need for asophisticated CPU for complicated computations. The existingstate-of-the-art methodology of obtaining a GPS position fixis, therefore, not suitable for many mobile sensing applicationssuch as livestock [5] and wildlife monitoring [6]; which neednon-intrusive position tracking support on resource constrainedplatforms (such as sensor nodes) for long durations.Application context and challenges. This paper is motivatedby the need to monitor megabats: flying foxes, a species that isresponsible for the spread of deadly diseases such as Hendra,Ebola, and SARS-like Coronavirus. For this application, theexisting platform (packaged as a collar) is a custom designedsmall, lightweight, battery powered, multi-modal sensing ca-pable wireless sensor node. It is severely constrained in termsof available energy resources required for sensing, processing,storage and communication; and can only harvest limitedenergy. It must collect data in a delay-tolerant way; and also becapable of long-term, unsupervised operation during which itmay not be in contact with the base station for data offloading.It uses GPS as the primary sensor for location tagging; whichis the best modality for outdoor localization, but leads to fasterenergy depletion than non-GPS aided sensing techniques [6].

With respect to delay-tolerant applications [5]–[7], existingsolutions provide coarse-grained GPS activity control. Theyconsider GPS as a black-box module, and tradeoff the energyexpense in deriving the position fix by adaptively using itwith other sensors [3]. Ramos et al. [8] and Liu et al. [9],by their recent LEAP and CO-GPS solutions, have shownthat significant energy savings can be achieved by exploitingthe coding nature of the GPS signal, and splitting the post-processing mechanism into local and cloud computation. Sucha solution offers a two-fold advantage of: (i) significant duty-cycling of the GPS device, as it only needs to run for a fewmilliseconds at a time to collect the most crucial informationfrom the satellites; and (ii) avoids the need for a powerful localCPU, by transferring raw data to the cloud and leveraging itsgreater processing power to calculate the location. While sucha data acquisition and processing model is well suited for thetarget application, the task of offloading data to the base station(or a cloud server) introduces an additional cost in energy.

Motivated by the need to limit this expenditure, we proposeSparse-GPS.Contribution. Sparse-GPS (or, S-GPS) is based on a mech-anism to compress and transmit the condensed GPS data tothe offloading device; wherein the coarse information of thecarrier frequency (from Doppler shifts), and time delay ofthe satellite signals can be efficiently recovered to determinethe visible satellites. Cross correlation is the conventionalmethod of obtaining these parameters2; but, given its sparseinformation content, we make use of the theoretical resultsin sparse approximation to achieve similar performance. Theunderlying information theory suggests that a signal can berecovered by `1-minimization [11], when its representation issufficiently sparse with respect to an over-complete dictionaryof base elements. The feasibility of such a mechanism wasfirst demonstrated by Misra et al. [12] for static ranging sce-narios with acoustic signals. However, recovering informationfrom compressed GPS (radio) signal is non-trivial due to itsvery weak signal strength, and two-dimensional (time delay,frequency shift) search mechanism.

In this paper, we overcome these challenges, and make thefollowing contributions.• We introduce Sparse-GPS, a new computing framework forenergy efficient GPS acquisition via sparse approximation.We propose a new dictionary that combines the informationsparsity along all search dimensions, and achieves up to twoorder of magnitude better sparse representation than standardDCT and FFT domains.• We analyze the dependency of the received signal-to-noiseratio and satellite acquisition count on data length. We showthat using a data length of 10-20 ms over 2 ms, there is a highprobability of acquiring 50% additional satellites with both theconventional and S-GPS method.• We demonstrate the GPS acquisition capability and energygains by empirical evaluations on real GPS signals. We showthat S-GPS is twice as energy efficient than offloading uncom-pressed data, and has 5-10 times lower energy cost than astandalone GPS; with a median positioning error of 40 m.In light of our contributions; we elaborate on the design of S-GPS in Section II, present its evaluation in Section III, surveyrelated work in Section IV, and summarize our work withconcluding remarks in Section V.

II. THE DESIGN OF S-GPS

A. Motivating Application

To ground our discussion, we consider the applicationcontext of monitoring flying foxes. Wildlife managers aregreatly interested in studying their ecology as flying foxesare the potential carriers of a number of infectious diseasesthat threaten livestock and humans; and are recognized asagricultural pests that cause damage to fruit crops worthmillions of dollars. In this regard, position tracking is animportant requirement for obtaining their roost camp locations,and also to understand their movement patterns (of which, littleis known).

2Another approach could be to calculate the cross-correlation result on thereceiver itself, and only offload the resultant coefficient. However, on-boardprocessing is still expensive as a large fraction (≈ 75%) of the GPS energyis consumed by this operation [10].

System architecture. The system is composed of three units.The mobile sensing unit consists of smart collars that aredeployed on flying foxes (typically, attached to the neck ofthe bat by trained, expert handlers). They are responsible forgathering and logging sensed data. The base station unit con-sists of resourceful gateway nodes that, on one hand, facilitateoffloading of data from the smart collars over a low-powerwireless radio connection; while on the other hand, uploadthe same to the central servers over a 2G/3G connection. Thisstatic infrastructure is placed at known bat roost camps, andcan be expanded as newer ones are discovered. The centralstorage and control servers form the final system unit wheredata is permanently stored, processed, and analyzed.Platform details. Each smart collar, with a combined weightof less than 30 g, incorporates a system-on-chip (SoC) with aGPS module [13]; inertial, acoustic, air pressure and temper-ature sensors; flash storage, two solar panels, and a 300 mAhLi-Ion battery. The SoC comprises of a microcontroller core,and an IEEE 802.15.4 complaint radio transceiver.Operational goals. Flying foxes are known to travelinto/across remote, inaccessible areas where cellular coveragemay not be available. The mobile sensing platform, therefore,must operate with high delay tolerance in collecting bothdaytime and nighttime position logs and operate over longperiods; until the bats return to the roost camps where thesensed data can be transfered to the base station. Hence, in thisapplication, energy is a critical resource and its conservationis greatly valued.Road-map. Of all the sensing units on the platform, GPS isthe most energy consuming module. For decreasing the energycost of obtaining a position fix, we adopt an approach similar toLiu et al. [9] where the raw GPS baseband signals are storedon-board, and the intensive location computation is delayedto the point in time when the data is uploaded to the centralservers. However, given the resource constraints, our key idea isto store compressed GPS samples that would translate to loweroffloading cost of energy over the low-power wireless radiocompared to its uncompressed case. In the following section,we present a crisp overview of the GPS receiving operationin order to identify unique features that can facilitate efficientcompression.

B. An Overview of GPS Receiving

The 32 GPS satellites continuously transmit CDMA codednavigational messages at a (low) data rate of 50 bps. Thisallows them to share the same carrier frequency of 1.575 GHz,and yet encode a different pseudo-random noise (PRN) se-quence. For civilian applications, each satellite uses a uniquesequence of 1023 bits (known as the course/acquisition, or C/Acode) that is transmitted at 1023 kbps. The C/A code, therefore,repeats every millisecond that results in 20 recurrences for eachdata bit sent.

A GPS receiver can calculate (or multilaterate [14]) itsposition by computing the travel time of the RF signalsfrom each (visible) satellite to itself, and combining it withthe respective satellites’ trajectories at the time. Consideringthe high (300 m/µs) propagation speed of RF waveforms,the receiver’s estimate of the time delay must be precise tothe microsecond level. The respective algorithm derives themillisecond (NMS) and sub-millisecond (subMS) part of the

propagation time differently; wherein the NMS is decoded fromthe packet frame (every 6 s), while the subMS is calculated bycorrelating the C/A code in the acquisition phase.GPS acquisition. It is, generally, the start-up mode in the post-processing chain3 that aims to determine the set of visiblesatellites. The presence of any of the 32 satellites can bedetected by identifying their unique 1023 bit C/A code; and isdone by cross-correlating the C/A codes in the received GPSsignal, typically shifted and scaled in time, with each known(C/A code) reference copy. Since the C/A codes are orthogonalto each other, any visible satellite will record a detectable spikein the correlation result. The motion of the satellites, however,introduces a Doppler shift in the received signal that needs tobe corrected.

In order to minimize the detection anomaly and success-fully decode the data from a given satellite, the acquisitionalgorithm performs a two dimension search on the receivedwaveform (say, x ∈ Rn); wherein, for each satellite, thelocally generated reference signal copy (say, p ∈ Rn) is cross-correlated with x. p ensembles combinational values from twodifferent sweeps:• over all possible 1023 code shifts τ• (minimum of) 41 equally spaced frequency bins ωd of width500 Hz within ±10 kHz of the center frequency ωc.The sequence r ∈ Rτ×ωd is the cross-correlation of p and x,and is defined as:

r =

n−1∑n=0

p[n− τ ]e−jωdnx[n] (1)

p is separately modulated by carriers e−jωdn and shifted intime. The center frequency of the respective bins in ωd aregiven as: [(ωc −∆ω), ..., (ωc + ∆ω)] where, ∆ω is referredto as the frequency bin width or search step. The maximumlikelihood estimate of (τ , ωd) (say, τ and ωd), which representthe subMS part of the propagation time and Doppler shift, isobtained by maximizing the function:

(τ , ωd) = arg max |r|2 (2)

Road-map. The operation of computing Eq. 2 is expensive,and demands high memory and energy resources. Consideringthe limited energy reserves on our target platform, it is desir-able to scale down its complexity by a simpler process whilestill being capable of precisely estimating (τ , ωd) during acqui-sition. This, coupled with the application-specific requirementsof high delay tolerance and data offloading support, raises thescope for a new framework.

Fig. 1 shows the correlation outputs, as given by Eq. 2,for a collected GPS trace. In theory, only one dominant peakshould be observed at the correct (code phase, frequency bin)combination; whereas, peaks of smaller magnitude may co-exist due to signal and noise interference. Fig. 1 exactly echoesthis predication, where the most dominant coefficient (or corre-lation peak) is the only useful information, and is representativeof the signal’s time delay and the Doppler shift. Therefore,our idea is to exploit the underlying information sparsity inthe signal model to design a simpler acquisition scheme thatsupports efficient compression, and later recovery. In the nextsection, we discuss the theory of sparse approximation that canexploit this sparse feature.

3If the existing position lock of satellites are within a second, the receivercan skip the acquisition process and directly start tracking.

Fig. 1: GPS acquisition by cross-correlation. The informationcontent is sparse as the value of the code phase (i.e., timedelay) and frequency bin (i.e., Doppler shift) corresponding tothe correlation peak is only useful.

C. An Overview of Sparse Approximation

Motivating insight. One can accurately and efficiently recoverthe information of a high dimensional signal (as x) from only asmall number of compressed measurements, when the signal-of-interest is sufficiently sparse in a certain transform domain[11], [15].

The sparsifying domain, referred to as a dictionary Ψ ∈Rn×d, is a collection of parametrized waveforms that expressx as a linear combination of a few significant elements. It isrepresented as:

x = Ψs =

d∑i=1

siψi (3)

where s ∈ Rd is a coefficient vector of x in the Ψ domain,and ψi is a column of Ψ. If s is sparse, then it is possibleto recover the position and value of its coefficients by acombinatorial problem; but is intractable. In pursuit of apolynomial time solution, Donoho [11] showed that, for a largesystem of equations, s can still be recovered by the following`1-minimization problem with high probability.

(`1) : s1 = arg min ‖s‖1 subject to: x = Ψs (4)

It has also been shown that dimensionality reduction by ran-dom linear projections preserves the `2 distance (i.e., all usefulinformation) in the projection domain [16]. `1-minimizationcan still be used to recover the sparse s from the projectedmeasurements with an overwhelming probability, even though,its dimension is significantly reduced. This operation can beachieved using a random sensing matrix Φ ∈ Rm×n as:

y = Φx = Φ(Ψs) = (ΦΨ)s (5)

where m � n and y ∈ Rm is the measurement vector.However, for recovery, the columns of (ΦΨ) should be asindependent as possible so that the information regarding eachcoefficient of s is contributed by a different direction; and thisis achievable if Φ and Ψ are more incoherent. Ensembles of

Base Station Server

- Acquire GPS signals- Compress and store

- Offload data - Acquisition: Sparse Approx.- Positioning: Modified CTN

Mobile Sensing Unit

Fig. 2: Architecture of S-GPS.

random matrices sampled independently and identically (i.i.d.)from Gaussian and ±1 Bernoulli distributions are largelyincoherent with any fixed dictionary Ψ, and therefore, permitcomputationally tractable recovery of s [11], [15].

D. Details of S-GPS

The critical aspect for casting the GPS acquisition probleminto the general framework of sparse approximation is todesign a sparsifying representation dictionary. In this section,we explain the architecture of S-GPS (Fig. 2) that supportsthe essential design principles to efficiently compress the GPSsignals on the target platform, offload to the base station,and facilitate GPS acquisition on the control server. Theback-end operation to convert the acquisition measurementsinto position coordinates leverages the modified coarse-timenavigation (CTN) technique [8], [9].

1) Design of Representation Dictionary:Design guidelines. The general criteria for designing a reliablerepresentation dictionary Ψ requires it to sufficiently sparsifythe signal x. However, the motion of transmitter (satellite)relative to the receiver introduces Doppler shifts that also needto be accounted during the GPS acquisition mechanism. This2D search over the delay-Doppler binned-space introduces animportant design criteria; where, Ψ should be able to preservethe propagation channel profile and frequency shift informa-tion while adhering to the basic design guidelines outlinedby the underlying theory. We also improvise an additionalcriteria where Ψ should facilitate a faster recovery mechanismthat implicitly derives the code phase and frequency binresults without reconstructing the original signal. Therefore,the design complexity is to identify and construct a befittingrepresentation dictionary that satisfies all of the aforesaidrequirements.Design intuition. To this end, we were guided by Eq. (1)where the locally generated reference copy ensembles valuesfrom two different sweeps: a frequency sweep over all possiblecarrier frequencies of IF±10 kHz in steps of 500 Hz (resultingin 41 frequency bins), and a code phase sweep over all 1023different code phases. This suggests that the received signal xcould be sparsely represented in the 2D delay-Doppler binned-space if we design a representation dictionary having columnelement that enumerate the C/A codes of the ith (where i ∈ {1-32}) satellite for each possible (codephase, frequency bin)combination.

Design execution. For realizing this design goal, we adopt acircular matrix design of Ψb ∈ Rn×1023 for each frequency binb. The columns of Ψb correspond to the 1023 different versionsof the C/A code (c1, c2, ..., c1023) with different code phasesmultiplied with respective phase points of the center frequencyof bin b. Ψb is of length of n corresponding to the length ofa complete code (i.e., 1 ms sampled at a chosen frequency).

For each satellite i, the coarse acquisition phase provides anestimate of the (code phase) delay τ and the Doppler shift ωd,which are integer multiples of the chip duration and frequencysearch step, respectively. One chip in the code is roughly1µs that converts to a delay measurement resolution of about300 m. Therefore, for obtaining a finer code phase precision,an oversampling factor λ is introduced into the design of Ψb

such that, for each frequency bin b, Ψb ∈ Rn×(λ×1023).Design types. Depending on the manner of solving for thecode phase, frequency bin and satellite, the following threesolution categories can be identified. We will evaluate thequality of three different dictionary designs in next section.• Multi-channel stacked. The key element in a multi-channeldesign (Fig. 3(a)) is to provision for independent channels,each dedicated to a satellite, that can be processed in parallel.For each satellite i, the algorithm needs to iterate over b bins,each with its respective Ψb. This, in fact, bears resemblanceto the native method of GPS acquisition.• Multi-channel flattened. For each satellite i, the dictionary isgiven by Ψi ∈ Rn×(b×λ×1023) (Fig. 3(b)); thereby replacing bdifferent instances of Ψb with a single flattened matrix Ψi.• Single-channel flattened. In contrast to the previous two de-signs, a single-channel design aims to process the informationfor all satellites at once (Fig. 3(c)). The dictionary is, therefore,given by Ψa ∈ Rn×(i×b×λ×1023).

2) Compression, Recovery and Acquisition: We adhere tothe same notation of p ∈ Rn and x ∈ Rn to represent thetransmitted and the received GPS signal vectors correspondingto 1 ms, for each satellite i.Compression. On the target platform, the dimensions of x aresignificantly reduced by multiplying it with a random sensingmatrix Φ ∈ Rm×n resulting in the measurement vector y ∈ Rm(m � n) as: y = Φx. m is related to n by the compressionfactor α given as: m = α n, where α ∈ [0, 1]. Φ is a binarysensing matrix with its entries i.i.d. sampled from a balancedsymmetric Bernoulli distribution of ±1. A balanced Φ consistsof ±1 at equal probability, where each row contains equalnumber of 1’s and -1’s. Therefore, in each row of Φ, thesum of the elements is always zero. A balanced Φ provides ahigher probability of detection (at recovery) if the noise in xis Gaussian [17]. The m samples of y are transferred to thebase station.Recovery via sparse approximation. The base station uploadsthe compressed measurements to a service application on thecontrol server. It requires the a-priori knowledge of the seedthat generates Φ, and the dictionary Ψ. Ψ ∈ {{b×Ψb},Ψi,Ψa}provides the representation basis where x can be sparselyrepresented by s4 as: x = Ψs. However, due to noise (whiteGaussian) v ∈ Rn present in real data, x may not be exactly

4Note: depending on the choice of Ψ, s provides a different result. Forexample: for Ψ ∈ Ψi, s specifies the joint (delay, Doppler) result for therespective satellite i; while, for Ψ ∈ Ψa, s provides the same pair of estimatesfor all 32 satellites.

(a) Multi-channel stacked (b) Multi-channel flattened

SAT: 01

Freq. Bin: 01

Code Phase:[1 … 1023]

Freq. Bin: [02-40]

Freq. Bin: 41

Code Phase:[1 … 1023]

SAT: 32

Freq. Bin: 01

Code Phase:[1 … 1023]

Freq. Bin: [02-40]

Freq. Bin: 41

Code Phase:[1 … 1023]

SATS: [02-31]

(c) Single-channel flattened

Fig. 3: Representation dictionary Ψ designs.

expressed as a sparse superposition of s; and so, x = Ψs + v,where v is bounded by ‖v‖2 < ε0. The sparse coefficientvector s is recovered by solving the following `1-minimizationproblem for a given tolerance ε via the second-order coneprogramming.:

(`1r) : s = arg min ‖s‖`1 s.t: ||ΦΨs− y||2 ≤ ε (6)

(`1r) is a stable and reduced version of `1-minimization. Itis known as Lasso in the statistical literature, and regularizeshighly undetermined linear systems when the desired solutionis sparse. Depending on the choice of Ψ, (`1r) needs to besolved individually for each satellite, or once for all satellites.

Input: Compressed measurements

L1r

L1r

ψ

Output: Indicator vector

PRN code generator

Local oscillator

90o

ψQФ

Generated once, and stored

Fig. 4: Search algorithm of S-GPS.

Acquisition. As explained earlier, Ψ is obtained by the mul-tiplication of the locally generated code sequences of therespective satellite(s) and the locally generated carrier signal.It is important to emphasis that the multiplication by a locallygenerated carrier signal produces the phase signal I, andmultiplication with its 90o phase-shifted version generates thequadrature signal Q. Therefore, Eq. 6 is solved with ΨI (i.e., in-phase part of Ψ) and ΨQ (i.e., quadrature-phase of Ψ) to obtain

the respective solutions sI and sQ. Finally, the summation ofthe point-wise absolute values of sI and sQ provide an estimateof s1 (Fig. 4).

As the C/A code is modulated onto the I part, the correctmatch should only be located in the I part of the signal.However, as the phase of the acquired signal is unknown, the Ipart of the signal generated at the satellite may not necessarilycorrespond to its recovered version. It is, therefore, importantto search across both the I and Q components of Ψ. Thelocation of the tallest peak in the coefficient vector s1 (alsoreferred to as the indicator vector: Fig. 4) provides an estimateof the propagation delay of the signal from the satellite(s) tothe receiver, and its respective Doppler shift.

E. Analysis of S-GPS

In this section, we analyze different dictionary designs,and also, the challenges in correctly and reliably identifyingthe visible satellites. Since our requirement was to modify themanner of GPS acquisition, standard black-box methods thatdirectly output the (code phase, frequency bin) informationwere not suitable.Experimental platform. We conduct this study (and furtherevaluations) using a SiGe GN3S v3 USB RF front-end [18].It consists of two integrated circuits: first, for RF amplifica-tion, filtering, down conversion, and baseband sampling; andsecond, for reading the digital samples (obtained from the firststage) and sending them in real-time to the PC through theUSB. The sampling frequency, intermediate frequency, andcapture data format of the front-end are user configurable. Thecaptured GPS data is then post-processed on the PC using asoftware-defined implementation of S-GPS.Data size. As the C/A code repeats every millisecond, 1 msof data is enough for acquiring satellites. However, as thedata packets are modulated by the C/A code at 50 bps, thereis a possibility of a bit transition every 20 ms. If this bittransition occurs in a 1 ms signal sample, there is a highpossibility of failure in acquiring the corresponding satellitedetails. Therefore, 2 ms chunk of data is more reliable forsatellite acquisition, and is widely adopted in practice [4], [8]–[10], [14].

1) Representation Dictionary: The multi-channel stackedmatrix design Ψ ∈ {b × Ψb} breaks down the joint (delay,Doppler) estimation problem, for each satellite, into b sub-problems (of smaller dimensions) that need to be solvedindependently. The b solutions are, subsequently, accumulatedto identify the position of the strongest coefficient. Such an

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Multi−channel Flattened

DCT

FFT

(b) Multi-channel flattened vs.{DCT & FFT}

Fig. 5: Comparison of sparsity levels. The signal-of-interesthas two order of magnitude more sparse representation inthe multi-channel flattened dictionary than the DCT and FFTdomains. Its combined (delay, Doppler) sparsity is also signif-icantly better than their respective individual levels providedby the multi-channel stacked dictionary. The figure has beenscaled down by a factor of 16 for clearer depiction.

approach results in b locally optimal solutions that may notnecessarily be the best (global) sparse representation of the(delay, Doppler) combination for the respective satellite. Thiscan be justified by Fig. 5(a) where the b stacked dictionariesare sparse in the representing the code phase delay, but not thefrequency bin.

The multi-channel flattened matrix design Ψ ∈ Ψi is acombined representation of the (delay, Doppler) sparsity foreach satellite, and facilitates their joint recovery by Eq. 6. Thesingle-channel flattened matrix design Ψ ∈ Ψa enhances theidea of jointly recovering all sparse information. It combinesthe (delay, Doppler) sparsity of all available GPS satellitesin one compact representation that can be solved at once byEq. 6. Although such as design is valid, our results showedthat the `1-minimizer gets biased towards the satellite withthe strongest signal; and hence, under performs in detectingremaining satellites with weaker signal levels. In terms ofmemory resources, Ψa needs 32 times more space than Ψi; andcan easily scale into ten of gigabytes or terabytes dependingon the choice of the oversampling factor λ. In this regard, Ψi

strikes a good tradeoff between sparsity and space complexity.Therefore, we adopt the multi-channel flattened Ψi design asthe representation dictionary5.

We evaluate the quality of the new dictionary, inherentlybased on the foundations of a circular matrix design; andalso, compare it against the popular DCT and FFT domains.A circular matrix is a special kind of Toeplitz matrix whereeach row vector is rotated one element to the right (or left)relative to the preceding row vector. In this regard, the designof Ψ for each Ψb bears similarity to the Toeplitz matrixdictionary proposed by Misra et al. [12]. However, their designdid not consider the effect of motion and Doppler errors; andhence, sparsely represents x only in the delay space but notin the Doppler space. Fig. 5 compares the sparsity levels ofx in the different representation dictionaries. The respectivecoefficients are sorted by their magnitude that decay like the

5The I and Q components of Ψi are generated once for all satellites, andstored; rather than repeated re-generations at runtime (Fig. 4).

Fig. 6: GPS acquisition by sparse approximation. Thequality of acquisition is the same as in Fig. 1 for the samedata set.

power law; i.e., the dth largest entry of the reordered s obeys|s|(d) ≤ Const·d−r for r ≥ 1. The fastest decay characteristicis observed in the multi-channel flattened dictionary. It offersthe most sparse representation; and hence, will facilitate themost accurate approximation of the sparse solution with thesmallest number of measurements. Here, it is important to notethat sparsity is a direct outcome of the design of the dictionary.

2) Acquisition Challenges and Mitigation:Basic performance test. Using 20 sets of raw GPS datataken from four different locations and time of the day,we analyze the satellite acquisition performance of S-GPSagainst SoftGNSS [14], a commercially available MATLABsupported software-defined GPS package. The acquiredsignals6 were compressed at different configurations ofα; ranging between 0.10-0.30 that translate to 90%-70%compression, respectively.

For illustration purpose, the acquisition quality of S-GPSwith 70% (i.e., α = 0.30) compressed measurement is shownin Fig. 6; with the same data set that was used for obtainingthe cross-correlation result shown in Fig. 1. We observethat both the methods yield the same result (code phase =515 chips and frequency bin index = 19) for the positionof the tallest spike. Although measurement noise leads toadditional correlation peaks of smaller magnitudes, they arenot important parameters for distance estimation.

A satellite was assumed to be acquired if the metricP, obtained by dividing the maximum/peak coefficient ins1 by the noise floor, exceeds a certain threshold T. Byempirical tests, we found that T greater than 5 was a reliablethreshold. On an average, S-GPS was able to correctly view2-3 satellites in each 2 ms chunk of every data segment, whilethe same was 2.5 times more for SoftGNSS. The tally of thedetected satellites was, therefore, considerably lower than theminimum count required for obtaining a GPS position fix.

6SiGe GN3S v2 front-end configuration: sampling frequency: 8.1838 MHz,intermediate frequency: 38.4 KHz, data format: 1bit real in short char binary

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(c)

Fig. 7: S-GPS acquisition challenges with 2 ms of data. (a):Low peak sharpness (i.e., ratio of the first to the second tallestpeak), and high recovery noise (b): Incorrect recovery (c): Lowpeak sharpness, but low recovery noise. The correct peak is atchip location (a)&(b): 4.8e+5 (c): 3.5e+5. Note: K = # datachunks of length 1 ms; α = compression factor.

We investigate the reasons for the unsatisfactoryperformance of S-GPS. We understand that GPS signalstrengths are, generally, very weak; and are in the range of18-25 dB below the noise level. While the signal is efficientlycaptured by a limited number of random measurements andis recovered by `1-min in the best possible manner, the lowSNR levels (especially below 20 dB) have a significant impacton the sparse approximation process. The higher measurementnoise contributes to either low peak sharpness (Fig. 7(a))or inaccurate recovery (Fig. 7(b)), which eventually lead tofailed or erroneous detection. Even for relatively strongersignals (that are slightly above 20 dB), the metric P mayclearly surpass the detection threshold; but still leaves scopefor further improvement to precisely recover the correct peakfrom the vicinity of near similar magnitude peaks (Fig. 7(c)).Although Fig. 7 shows the observation from α=0.20, similaroutcomes were also logged for α=0.10 and α=0.30.Improving acquisition reliability. A simple solution toovercome the satellite detection anomalies is to boost themagnitude of the correct peak coefficient, which is anapproximate indication of the SNR, with respect to the noisefloor. We, therefore, append a SNR improvement stage tothe S-GPS framework. We calculate the consolidated pointby the accumulation of K coefficient vectors (where each Kcorresponds to the recovery result of 1 ms of GPS data), andsumming their intensities.

sc =

K∑k=1

(s1)k (7)

Satellite i is said to be detected if the metric Pc, obtainedby dividing the maximum coefficient in sc by the noise floor,exceeds the threshold T. This operation is performed for all isatellites.

As mentioned before, the navigational data is transmittedat a rate of 50 bps; and therefore, will result in a possible bittransition every 20 ms. This method also provides robustness tothe negative effect of transitions in the data bits; as it considersthe accumulated and summed contributions over a longer time-window rather than analyzing individual 1 ms data segments.

Fig. 8 demonstrates the benefits of this mechanism. For α= 0.20, K = 2 does not correctly recover the index of the peakcoefficient (Fig. 8(a)); but as K is increased to 6 by combiningthe contribution of six 1 ms chunks, the estimation becomesmore accurate (Fig. 8(b)). The problem of the high noise floor,which is still evident at this stage, is significantly reduced as K

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Fig. 8: Improving acquisition reliability. Consolidating thecoefficient vector points over K operations improves the mag-nitude of the correct peak coefficient with respect to the noisefloor. For all the cases, the correct peak is at chip location:4.8e+5.

reaches 10 (Fig. 8(c)). The same observations are also valid fora higher α of 0.30 and K = 2 (Fig. 8(d)). However, estimationreliability is attained at K = 6 (Fig. 8(e)) without any significantimprovements with additional contributions (Fig. 8(f)). It isimportant to note that K is also indicative of the correspondingdata length to be processed. For example, K = 6 is theconsolidated result obtained by processing 6 data chunks of1 ms length; or a combined data length of 6 ms.

III. EVALUATION

In this section, we evaluate the quality and limitations ofthe S-GPS framework.Setup. This study uses 20 sets of raw GPS data, collectedusing the experimentation platform described in Section II-E. Itoffered the flexibility of varying both the GPS signal (between10-60 s) and sample length with configurable parameters. Also,as mentioned before, the ground-truth was obtained withSoftGNSS.

When considering the presented results, it is important tonote the categorical difference of S-GPS from the state-of-the-art acquisition method; where our aim is to attain similarperformance, but with significantly fewer observations. Whilesuch a requirement may not arise in regular applications, it is anecessity in our motivating application and other related ones.

S-GPS aims to achieve the best possible energy efficiencyin data offloading and GPS sensing. In this regard, data sizeis a key parameter that determines a good tradeoff betweenaccuracy and energy.

A. Acquisition and Location Performance

Acquisition quality. The purpose of acquisition is to identifyall visible satellites (along with their respective code phasedelay and frequency shifts); since, acquiring more satellitesimproves the overall location accuracy. Therefore, as a func-tional goal, any GPS acquisition algorithm must maximize theprobability of successful satellite acquisitions.

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Fig. 9: Acquisition quality. (a): Benefits of processing longer segments. There is a high probability of acquiring an additional1.5× satellites by processing 10-20 ms over 2 ms. (b)&(c): Acquisition quality of S-GPS, for different data length {10-20}ms,at compression factor of {0.10,0.20,0.30}. Note: K = 20 is the consolidated result obtained by processing 20 data chunks of1 ms length; and therefore, K is also an indicator of the data length.

In this regard, an important question is whether processinglonger data lengths (such as 10/20 ms) promises better acqui-sition quality than the accepted practice of using 2 ms. Theresult for this study, using the state-of-the-art cross-correlationmethod, is shown in Fig. 9(a); and it suggests that thereis a 95% probability of detecting 1.5× more satellites byprocessing longer data segments. We also observe the sameresults with S-GPS as depicted in Fig. 9(b) and Fig. 9(c).

While such a mechanism may not be a good alternativefor on-board acquisitions (as they are more energy consumingdue to greater computational demand and processing time), itcan be more viable if the computation load can be transferredto the control server. Also, in applications such as trackingflying foxes, there may not be any previous knowledge aboutthe visit locations or their approximate perimeters. In sucha scenario, it is difficult to predict the acquisition quality.Therefore, considering the limited reserves of energy, it maybe a good choice to safeguard against failed acquisitions bycollecting longer data chunks.

With this background, we investigate a reliable data sizemeasure that optimizes energy and acquisition quality of S-GPS. Fig. 9(b) & Fig. 9(c) characterizes the tradeoff betweencompression factor (α) and accumulated contribution from K(1 ms) chunks against the number of satellites acquired. Theoptimal choice of α and K is important to ascertain the bestacquisition performance that can be achieved with the leastmeasurements m (refer to Section II-D2), where a smaller mleads to lower storage and transmission cost.

Fig. 9(b) shows the absolute satellite count with differentα and K; and suggests that their lower values result indeteriorated performance. α = 0.10 (for any K) is, typically,not useful as it does not meet the minimum tally of (at least 5)satellites for obtaining a position fix with the modified CTNmethod; while α = 0.20 for (K = 12-20) and α = 0.30for (K = 10-20) meet this criteria. However, neither of theseparameter choices are able to mirror the ground truth resultof 8 satellites. Fig. 9(c) shows the ratio of the number ofdetected satellites using compressed data of length (α× K) msto its respective uncompressed K ms case. A ratio of 1 impliesthat the performance of the compressed case is similar to its

uncompressed counterpart. However, the results suggest thatthe best outcome is only 0.8; and is obtained at α = 0.20 for(K = 18-20) α = 0.30 for (K = 12-20). This means that S-GPSdetects 1-2 fewer satellite(s) than its ground truth.

The above studies, however, do not make a fair comparisonbased on the absolute data length. For example, data com-pressed with α = 0.20 and K = 20 and α = 0.30 and K = 20have an absolute length of 4 ms and 6 ms, respectively. There-fore, they would not derive the same performance indicators astheir uncompressed 20 ms segment. Fig. 10(a) and Fig. 10(b)make the direct comparison, and express it as a ratio of [(0.20×K)/4 ms] and [(0.20× K)/6 ms], respectively. Both the resultssuggest that there is a 95% probability of detecting 1.2×more satellites by recording 20 ms and compressing it down to4 ms/6 ms; rather than simply processing their uncompressedversion of equivalenty data length. This improvement is aresult of information embedding in random ensembles; whichpreserves the energy of its respective higher dimension (i.e.,20 ms) representation, although the absolute data length issignificantly reduced by 70-80%.

Alternately, for acquiring the same number of satellites astheir equivalent uncompressed data lengths, there is a 95%probability of success by using as low as K = 12 for α = 0.20and K = 10 for α = 0.30. These parameters translate to a40-50% savings on the required data size for mirroring theacquisition quality as the ground truth. Fig. 10(e) shows theoptimal configuration of α and K, as suggested by Fig. 10(a)and Fig. 10(b), for obtaining a similar acquisition quality astheir uncompressed (base) cases of 4 ms and 6 ms.Location accuracy. Fig. 10(c) and Fig. 10(d) shows a box-plotof the overall location accuracy for α = 0.20 and α = 0.30. Forthe respective cases, the median error (depicted as a blue ‘o’)is less than 70 m and 40 m. Although the median error is quiteconsistent across all cases, the interquartile range shows somevariations due to the non-uniform tally of acquired satellitesin each configuration and data points. Fig. 10(f) groups theobservations according to the visible satellites count (that varyfrom 5-7), and shows the corresponding error in location. AsS-GPS also uses the modified CTN technique for positioning,a minimum of 5 satellites are required. The accuracy improves

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Fig. 11: Energy consumption. S-GPS is twice as energy efficient than CO-GPS, and has 5-10 times lower energy costs than astandalone GPS. S-GPS and CO-GPS consume a few µJ due to their very small sensing cycles; and so, the radio is the majorcontributor to the energy cost for cloud-offloading solutions.

from a median error of 70 m to 30 m with the availability ofmore satellites. The location accuracy of S-GPS is similar toLEAP and CO-GPS (< 35-40 m), and also duly satisfies ourapplication’s requirement.

B. Energy consumption

We provide an estimate of the GPS acquisition cost, interms of energy budget, on the target platform for obtaining asingle position fix.Components evaluated. In our study, we used the approach ofcapturing digitized GPS samples; followed by their compres-sion by random ensembles with its entries i.i.d. sampled from abalanced symmetric (± 1) Bernoulli distribution. However, aspart of a efficient GPS receiver system, this entire step can besubstituted by a compressed sensing analog front-end (referredto as: CS-ADC). A CS-ADC can sample sparse signals at sub-Nyquist rates, and deliver compressed measurements directly.Many existing hardware prototypes of a CS-ADC have shownthat its power consumption is less than a traditional analog-to-digital converter [19], [20] as it does not have to sample at

the full (Nyquist) rate. Considering these empirical facts, weonly evaluate the energy costs of the two most power intensivemodules on the platform: (i) u-blox MAX-6 GPS [13] and (ii)IEEE 802.15.4 complaint radio transceiver that, respectively,consume 74 mW and 99 mW in full operation mode. Previouswork by Sommer et al. [21] and Afanasyev et al. [22] havereported that the data goodput of IEEE 802.15.4 complainttransceivers are between 42 kbps and 93.6 kbps; while the GPS(coldstart and hotstart) time-to-first-fix is 26 s.

Taking all of the above empirical observations into account,we show the corresponding energy consumption in Fig. 11.S-GPS is able to achieve a competing level of acquisitionperformance at K = 12 for α = 0.20 and K = 10 for α =0.30 over its respective uncompressed case of sensing 4 ms and6 ms of raw data. S-GPS is 1.8 times (at K = 12 for α = 0.20)and 2 times (at K = 10 for α) more energy efficient than CO-GPS, which is based on a simple sense and offload paradigm.In comparison to a standalone GPS module, which performsall operations on the platform itself without optimized sensingand offload cycles; S-GPS saves 5-10 times more energy.

LZ777 S-GPS0

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Road-map. Based on the results of acquisition quality, locationaccuracy and energy cost, a compression factor of 0.30 andK=10 (i.e., a combined data length of 10 ms) is a reliableconfiguration for S-GPS.

C. Compression Performance

Fig. 12 compares the compression quality of S-GPS againstthe popular LZ77-based algorithm ‘gzip’. The result showsthat raw GPS signals are not much compressible (< 10%)using traditional methods such as LZ77 (since they appearlike random noise by design); while the same signals can becompressed by 70% with S-GPS. Besides, the LZ77 losslessnature of compression makes it nonrobust to information loss(packet drops) during data transmission that are common inlow-power sensor networks. On the other hand, the S-GPSwould offer a graceful performance degradation under similarcircumstances as it can still recover the results, but with largererrors; and has the same performance as compressing with asmaller α.

IV. RELATED WORK

Location sensing, by itself, is a rich area of research; andperforming it with GPS is an active topic of investigation.S-GPS draws on prior work in multiple areas; mainly publicinfrastructure based outdoor mobile sensing, signal synchro-nization, cloud offloading based GPS, and sparse approxima-tion.

The use of public infrastructure (such as GPS [23], A-GPS [24], WiFi access points [25], FM radio stations [26],Cellular towers, etc.,) is an appealing direction as it relaxesthe need to deploy systems (such as wireless sensor nodes[27] and other embedded platforms [28]) for localizationassistance, and can cater to a wider range of outdoor (real-time and delay-tolerant [7]) applications. The mobile receiverssimply needs to synchronize their operation with the respectiveinfrastructure system counterpart. Although the problem ofsignal synchronization applies to many of the above wirelesstechnologies, synchronizing with GPS satellites is processing-intensive and energy consuming; due to its nature of operation(i.e., two-dimension search using cross-correlation) and verylow (−20 dB) SNR [4]. WiFi and Cellular systems operateat much higher levels of SNR than GPS; and hence, the

receivers can synchronize with relatively low overhead bymerely detecting an increase in received power [29].

Several techniques have been proposed to address the prob-lem of energy consumption in GPS receiving. Many of thesesolutions are designed with a focus on real-time applications,and also consider GPS as a potential black-box. They tradeoffenergy expense by adaptively using it with other sensors [3],turning it on when significant motion is detected [2], or bycombining location requests from multiple applications witha single GPS reading [30]. Although these solutions can alsobe used for delay-tolerant applications, they do not improviseon the time-flexible nature to optimize the de facto GPS post-processing chain and/or aggressively duty-cycle.

In pursuit of a mechanism to reduce the active GPS time,LEAP [8] and CO-GPS [9] solutions combine these benefitsfor applications of delay-tolerant nature. LEAP performs GPSacquisition on the receiver locally, and transfers the resultinginformation to the cloud. The location is computed on thecloud server with the CTN technique, wherein the preliminaryacquisition results are combined with a known location of anearby object (e.g., the cell tower in case of a phone). Asthis solution cannot be used for embedded platforms withoutcellular connection (for providing landmarks) and limitedcomputation resources (for performing acquisition); CO-GPStransfers the required raw signal samples for acquisition tothe cloud, and uses its vast computing resources to guesscandidate landmarks and maintain the ephemeris database forpositioning. S-GPS adopts the sample-and-process approach ofCO-GPS, but reduces the energy cost of data offloading.

S-GPS, based on the theory of sparse approximation, takesadvantage of information sparsity in the GPS acquisitionprocess. The information is efficiently embedded without muchloss (which serves the purpose of storage and transmission),and is subsequently recovered from an underdetermined systemby `1-minimization. Sparsity aware solutions offer an efficientsampling strategy; and so, are an active field of appliedresearch in resource constrained sensor networks [12], [31].Although S-GPS falls into the category of sparse approxima-tion based range-finders as previously investigated by Misra etal. [12], the scope of our problem is completely different. Wedesign a new dictionary and related suite of signal processingtechniques for GPS acquisition that estimate the propagationdelay from the satellites to the receiver; while compensatingfor Doppler effect and very low SNR levels. QuickSync [10]belongs to the class of real-time solutions, which aim to reducethe GPS synchronization time on the receiver itself by sparseFourier transform. Therefore, there are fundamental differencesin theory and application scope; although, the idea of sparsityis central to both S-GPS and QuickSync.

V. CONCLUSION

For delay-tolerant applications, offloading GPS processingto the cloud is possible. S-GPS is a GPS sensing approach thatis aimed to limit the associated energy costs in this transferoperation. The sparse representation based GPS acquisitiontechnique can efficiently capture and embed information ina lower dimensional space (by random ensembles); and sub-sequently, recover it from an underdetermined system. Suchan approach has several merits. It provides a simple dimen-sionality reduction mechanism to condense the dataset. As thedata compressibility is proportional to its information level,

sparse (information) signals can be compressed significantly.It requires transferring and processing a significantly smallerdatasets to obtain accuracies comparable to the state-of-the-artdetection technique. At the local device end, the simplicity ofthis operation translates into appreciable energy savings. Byempirical evaluations, we showed that S-GPS is 2 times moreenergy efficient than offloading uncompressed data, and has5-10 times lower energy costs than a standalone GPS; with amedian positioning accuracy of 40 m.

S-GPS would further benefit by mechanisms to enhancethe received SNR; which was, by far, the most dauntingtask in realizing this solution. The initial success of S-GPShas motivated us to explore efficient hardware designs forcompression on the target platform. In addition, we are alsofocusing on techniques to optimize the energy expenditure andexecution time on the server side.

VI. ACKNOWLEDGEMENT

This work was performed by P. Misra during the tenureof an ERCIM ‘Alain Bensoussan’ Fellowship Programme. Theresearch leading to these results have received funding from theEuropean Union Seventh Framework Programme(FP7/2007-2013) under grant agreement no. 246016. We would like tothank the anonymous reviewers, and our shepherd Dr. NikiTrigoni (University of Oxford) for their helpful comments.

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